Giải thích các bước giải:
Ta có:
$\sin a=\dfrac35$
$\to \cos^2a=1-\sin^2a=\dfrac{16}{25}$
Mà $\dfrac{\pi}{2}<a<\pi \to \cos a<0$
$\to \cos a=-\dfrac45$
Ta có:
$\cos(a+\dfrac23\pi)=\cos a\cos(\dfrac23\pi)-\sin a\sin(\dfrac23\pi)$
$\to \cos(a+\dfrac23\pi)=-\dfrac45\cdot (-\dfrac12)-\dfrac35\cdot \dfrac{\sqrt{3}}{2}$
$\to \cos(a+\dfrac23\pi)=\dfrac{4-3\sqrt3}{10}$